>>11233766It's the rate of change of curvature. Say you have a smooth and continuous function on (A,B). That function can be graphed. The curvature at any point along that graph can be thought of as 1/R where R is the radius of the circle that just barely kisses (osculates) with that point. If the third derivative is positive, that means the curvature is increasing locally. That means the graph will intersect the osculating circle. If curvature is not increasing, the circle is not intersected.